I recently read an article on Wired about the Solar Voyager. A pair of engineers, Isaac Penny and Christopher Sam Soon, designed and built an autonomous, solar powered vessel. On June 1st, 2016 the 18 foot vessel, named Solar Voyager set off on its trans-Atlantic adventure from Gloucester, Massachusetts to Portugal, a journey of more than 4800 kilometres. They are predicting that this trip will take 4 months, assuming that there are no catastrophic events mid-Atlantic. One cool thing about this trip is that the Solar Voyager reports it position and other data online every 15 minutes at ​http://www.solar-voyager.com/trackatlantic.html. Currently, about two-weeks into its journey, Solar Voyager is just South of Halifax, Nova Scotia where I live.

Photo from Isaac Penny/The Solar Voyager Team

The image below shows how far the Solar Voyager has traveled during its first two weeks. That is 1/8 of the time estimated for the crossing. Based on the information below, do you think that it will reach its destination in 4 months? What factors did you consider when making your estimation?

Some factors you might consider are currents, weather, equipment malfunction, obstacles/collisions, wear and tear, etc. There are so many variables at play that it must be very hard to make an accurate estimation.

Some Questions/Estimates for Students:

Estimate the probability that Solar Voyager will reach Portugal in 4 months.

Estimate the probability that Solar Voyager completes its journey (i.e. it doesn't sink or malfunction). You could make these predictions and check up on them when you come back to school in the fall.

Do you think that the vessels progress is/will be modeled by a linear function? Is it likely to get faster, slower or progress at the same rate over time?

What is the scale factor of this 18 foot vessel to a typical cargo vessel?

One of the coolest things about this project is that these young engineers "built Solar Voyager in their free time, undertaking this voyage simply for the challenge." How can I commandeer this type of intrinsic motivation for students in math class? What about this project made them want to work so hard "just for the challenge" and not for some extrinsic reward. Was it because they were the ones who selected and designed the task? Did they have just the right skills so that they felt confident that they would be successful? What is something that was relevant to their lives? How did this project captivate their curiosity?

My son and I walked through the train station in Halifax this morning. We were across the street at the Halifax Seaport Farmers' Market and he wanted to see if there was a train at the station. No train this morning but the schedule shows that one is coming in later this evening. The Ocean is the name of the Via Rail train that travels between Halifax and Montréal. It makes stops at a lot of stations in between as well.

What sort of questions might your students have about this train schedule? How long is this train at the station during a typical week? If this train is at the station in Montréal for a similar amount of time, then how long is each trip from Halifax to Montréal? What is the average speed of this train during its trip? What do you think the schedule looks like that is posted at the station in Montréal? How would this trip via train compare to a trip via car or plane (time, cost, etc.)?

As a math teacher, I always love to see folks doing real math on television. Last week, on The Amazing Race Canada (Season 3, Episode 7), there was a 'tricky' mathematical challenge. Contestants were given a list of Air Canada flights and asked to create a flight plan using Air Canada destinations from around the world. They had to find a set of flights that had a total flight time of 25 hours (or 1500 minutes). They also had to ensure they used "a combination of routes that travel to at least three continents". Calculating the flight time was the first hurdle. Since arrival and departures are listed in local time and the vast majority of these flights crossed multiple time zones, contestants had to use the universal time code for each city to correct for time changes. A number of teams were confused right from the start (there was a lot of fixed mindset talk from the contestants). One team used an 'Express Pass' to skip this challenge while two other teams gave up and took a 2 hour time penalty instead of continuing with the challenge,

The Flight Boards - From Season 3, Episode 7 of The Amazing Race Canada

That is a lot of flights! There are 12 flights listed on the Europe board, 11 flights on the Asia Pacific board and 15 flights on The Americas board. If we use just one flight from each board (so that we visit three continents), there are a total of 1980 combinations (12*11*15=1980). The rules state that we have to visit at least three continents but it doesn't say how many flight to use so we could have a flight plan with more than three flights. If we add one additional flight to make a flight plan with four flights, now we have 69300 possible flight plans (12*11*15*35=69300... one flight from each board and any one of the remaining 35 flights). That is a LOT of trial and error. The two solutions shown on the episode contained 4 flights. Are there any 3 flight plans that would work? Here is what I did.

First I got some screen captures of the flight boards so I could read all the flight times. Then I put them all into an Excel spreadsheet to calculate the flight times in minutes. Next I played with Excel for about an hour to try to find an efficient way to calculate all the combinations of flights that I wanted to try and then gave up. Instead, I created a quick program in Python to calculate all the possible sets with just three flight plans. This turned out to be much easier than using Excel (just 8 lines of code).

I found about 16 flight plans total that used a set of 4 flights. Not a whole lot for 69300 possible combinations. The probability of find a flight using a random guess would be 16/69300 = pretty small. Given that it takes time to add up the four numbers, even using a calculator, random guessing would not be a great choice. You can use some strategy to narrow down the possibilities. For example, you know that the total has to equal 1500 minutes so you can focus on just the last two digits and the possible flights that can get you to a multiple of 100. Any other suggestions for strategies to speed this up? The episode didn't show how long it took the teams to complete the task, but three groups (6 people) teamed up to tackle this problem in order to find just one solution. One team, the last team to finish, persevered and found a solution all by themselves. The team that lost was one that took the two hour time penalty so we can assume that this challenge took them less to two hours (or pretty close to that) to complete.

That is a lot of math!

There was a nice article posted online that interviewed the Air Canada captain that handed out the clue cards for the challenge. He mentions the factors that he said made this such a challenging competition.